Gravity Gradient Measurements Research Articles

High-order gravitational gradient effect in the gravity gradient measurement by the Eötvös-type torsion balance

High-order gravitational gradient effect in the gravity gradient measurement by the Eötvös-type torsion balance

Joint inversion of gravity and gravity gradient data using smoothed L0 norm regularization algorithm with sensitivity matrix compression

Improving efficiency and accuracy are critical issues in geophysical inversion. In this study, a new algorithm is proposed for the joint inversion of gravity and gravity gradient data. Based on the regularization theory, the objective function is constructed using smoothed L0 norm (SL0), then the optimal solution is obtained by the non-linear conjugate gradient method. Numerical modeling shows that our algorithm is much more efficient than the conventional SL0 based on the sparse theory, especially when inverting large-scale data, and also has better anti-noise performance while preserving its advantage of high accuracy. Compressing the sensitivity matrices has further improved efficiency, and introducing the data weighting and the self-adaptive regularization parameter has improved the convergence rate of the inversion. Moreover, the impacts of the depth weighting, model weighting, and density constraint are also analyzed. Finally, our algorithm is applied to the gravity and gravity gradient measurements at the Vinton salt dome. The inverted distribution range, thickness, and geometry of the cap rock are in good agreement with previous studies based on geological data, drilling data, seismic data, etc., validating the feasibility of this algorithm in actual geological conditions.

Experimental analysis of the performance of a new shipboard gravity gradient measurement system

The gravity gradient tensor, which has a higher resolution than gravity, is used in a variety of fields, including the discovery of energy resources, auxiliary navigation, and national defense building. Our team has achieved significant advancements in various essential technologies, such as high-resolution accelerometers, and has constructed China’s first self-controllable shipboard gravity gradient measurement system. In the laboratory, accuracy is determined using the mass gravitation technique, static test accuracy of Tuv and Txy is 7.22 E and 3.58 E, while dynamic test accuracy of Tuv and Txy is 9.09 E and 4.16 E. For outfield shipborne test measurement, the internal accord accuracy of Tuv and Txy of the repeat line is 28.2E@750m and 28.8E@750m, and that of the intersection point is 28.2E@750m and 26.8E@750m. The performance of the system is completely validated by dynamic and static testing, laying the groundwork for the practical implementation of gravity gradient technology.

Autonomous navigation for lunar final approach based on gravity gradient measurements

Lunar final approach navigation is critical for pin-point lunar landing in future missions. This study investigates the use of lunar gravity gradient measurements for autonomous navigation of a lunar probe during the final approach phase. As the spacecraft approaches the Moon, the strength of gravity gradient signals improves. A spaceborne gravity gradiometer can precisely measure local gravity gradients, and the latest lunar gravity model GL1500E is used to provide reference values. The employed truncation degree and order of the gravity model are increased stepwise considering the decreasing altitude of the spacecraft in order to reach a compromise between computational costs and model accuracy. An iterative Kalman filter is developed for coupled orbit and attitude estimation using gravity gradient measurements and attitude quaternions obtained from star sensors. A simulated spacecraft with a gradiometer noise level of 0.01 E is considered. Simulation results show that the spacecraft’s position converges rapidly and achieves an accuracy of less than 100 m at the last epoch.

Influence of Sea Level Anomaly on Underwater Gravity Gradient Measurements.

Considering the theoretical research needs of gravity gradient detection and navigation, this study uses the right rectangular prism method to calculate the disturbing gravity gradient from sea level anomalies in the range of 5° × 5° in the Kuroshio extension area of the western Pacific with large sea level anomalies. The disturbing gravity gradient is obtained in different directions within a depth of 50 m below the mean sea level based on the principle of the disturbing gravity gradient. The calculation results show that the sea level anomalies at local positions significantly impact the underwater gravity gradient measurements, with the maximum contribution exceeding 10 E and the maximum difference between different locations exceeding 20 E. The change of the sea level anomaly over time also significantly impacts the measurement of the underwater gravity gradient, with the maximum change value exceeding 20 E. The impact will have a corresponding change with the seasonal change of the sea level anomaly. Therefore, the underwater carrier needs to consider the disturbing gravity gradient caused by sea level anomalies when using the gravity gradient for underwater detection and navigation.

3D probabilistic geology differentiation based on airborne geophysics, mixed Lp norm joint inversion, and physical property measurements

The physical property models obtained from geophysical inversions can be converted to a 3D quasi-geology model via a process called geology differentiation. Recent works indicate that the geology differentiation can help maximize the value of the information contained in geophysical data. However, it remains largely unexplored as to how to quantify the uncertainties of a 3D quasi-geology model. We approach this problem by using a recently developed mixed [Formula: see text] norm regularization and a priori physical property measurements. We use mixed [Formula: see text] norm joint inversion to construct a large sequence of physical property models based on the Gzz component of the airborne gravity gradient and magnetic measurements. The available physical property measurements are used to determine which physical property models to accept. We then construct a sequence of 3D quasi-geology models by performing the geology differentiation for all of the accepted models, which allows us to compute the probabilities of our geology differentiation results. We apply our approach to a set of field data collected over the Decorah area located in northeast Iowa. We successfully quantify the uncertainties of the spatial extents for the identified geologic units and compute probabilities of geologic units at any location in our study area. The proposed workflow has broad implications for 3D geologic model building based on multiple geophysical and/or rock sample measurements.

Position fixing with cold atom gravity gradiometers

This paper proposes a position fixing method for autonomous navigation using partial gravity gradient solutions from cold atom interferometers. Cold atom quantum sensors can provide ultra-precise measurements of inertial quantities, such as acceleration and rotation rates. However, we investigate the use of pairs of cold atom interferometers to measure the local gravity gradient and to provide position information by referencing these measurements against a suitable database. Simulating the motion of a vehicle, we use partial gravity gradient measurements to reduce the positional drift associated with inertial navigation systems. Using standard open source global gravity databases, we show stable navigation solutions for trajectories of over 1000 km.

ОПЫТНО-МЕТОДИЧЕСКИЕ РАБОТЫ ПО ИЗМЕРЕНИЮ ЗНАЧЕНИЙ СИЛЫ ТЯЖЕСТИ И ЕЕ ВЕРТИКАЛЬНОГО ГРАДИЕНТА

The article describes the methodology of field work on gravity surveying and measurement of the vertical gravity gradient using a high-precision gravimeter. The processing teqnique of received data by the Geosoft Oasis Montaj software package (Canada) is described. Research results, conclusions and recommendations for the performance of such works by the method of multi-level measurements of gravity values are presented.

Interferometry in an Atomic Fountain with Ytterbium Bose–Einstein Condensates

We present enabling experimental tools and atom interferometer implementations in a vertical “fountain” geometry with ytterbium Bose–Einstein condensates. To meet the unique challenge of the heavy, non-magnetic atom, we apply a shaped optical potential to balance against gravity following evaporative cooling and demonstrate a double Mach–Zehnder interferometer suitable for applications such as gravity gradient measurements. Furthermore, we also investigate the use of a pulsed optical potential to act as a matter wave lens in the vertical direction during expansion of the Bose–Einstein condensate. This method is shown to be even more effective than the aforementioned shaped optical potential. The application of this method results in a reduction of velocity spread (or equivalently an increase in source brightness) of more than a factor of five, which we demonstrate using a two-pulse momentum-space Ramsey interferometer. The vertical geometry implementation of our diffraction beams ensures that the atomic center of mass maintains overlap with the pulsed atom optical elements, thus allowing extension of atom interferometer times beyond what is possible in a horizontal geometry. Our results thus provide useful tools for enhancing the precision of atom interferometry with ultracold ytterbium atoms.

A torque type full tensor gravity gradiometer based on a flexure-strip suspension.

Full tensor gravity gradiometers based on accelerometer pair combination are widely employed in earth resource explorations using gravity gradient measurements. However, the extremely high requirements of accelerometer dynamic range and the scale factor consistency of accelerometer pairs are the two main limitations to further improve their performances. In order to overcome these two extreme challenges, the torque type gravity gradiometer based on the Etövös torsion balance pendulum is re-considered. In this paper, an improved torque type full tensor gravity gradiometer with a flexure-strip suspension is proposed, which balances the mechanical sensitivity and the response time. The proposed gradiometer can be used to measure the full tensor gravity gradient by observing angle variations at three azimuths. The principle and feasibility of the torque type full tensor gravity gradiometer based on a flexure-strip suspension are introduced, and the main noise sources including mechanical thermal noise, position sensing noise, and readout noise are analyzed. A prototype gravity gradiometer with a designed resolution of 2 E/Hz1/2 at 0.1 Hz is constructed (1 E = 10-9/s2), and the experimental results indicate that its resolution comes to 3 E/Hz1/2 at 0.1 Hz, which is mainly limited by the seismic noise. This type of gravity gradiometer can be further improved due to its high potential resolution and independence of matching combination requirement, which allows it to be applied in next generation gravity resource exploration.

Using non-diagonal data covariances in geophysical inversion

SUMMARY We present a new approach that allows for the inversion of quantities derived from the observed data using non-diagonal data covariance matrices. For example, we can invert approximations of apparent resistivity and phase instead of magnetotelluric impedance using this methodology. Compared to the direct inversion of these derived quantities, the proposed methodology has two advantages: (i) If an inversion algorithm allows for the specification of a full data covariance matrix, users can invert for arbitrary derived quantities by specifying the appropriate covariance matrix instead of having to rely on the inversion code to have implemented this feature. (ii) It is fully compatible with the assumptions of least-squares optimization and thus avoids potential issues with bias when inverting quantities that are nonlinear functions of the original data, We discuss the theory of this approach and show an example using magnetotelluric data. However, the same method can be applied to other types of geophysical data, for example gravity gradient measurements.

Evaluation of global gravity models from absolute gravity and vertical gravity gradient measurements in Turkey

A global gravity model (GGM) is a mathematical function describing the gravity field of the Earth. The assessment of GGMs involves identifying the best-fitting model to local gravity field for geodetic and geophysical applications. Thus, highly accurate independent datasets are required to obtain the appropriate model. In general, GPS/levelling data have been used for this purpose. If these measurements are not performed simultaneously, they may not be reliable due to vertical deformations especially in seismically active countries. Therefore, we used highly precise absolute and vertical gravity gradient measurements obtained by the Scientific and Technological Research Council of Turkey’s (TUBITAK) National Metrology Institute and General Directorate of Mapping within the frame of Turkish Height System Modernization and Gravity Recovery Project over the period of 2016–2018 from Turkey to choose the best GGM for the whole of Turkey among the 19 latest tested satellite-only and combined GGMs (2004–2018). Our results showed that vertical gravity gradient measurements could also be used for the regional validation of GGMs as an independent in situ dataset. The GOCE based XGM2016 combined model and GO_CONS_GCF_2_TIM_R5 satellite-based model were found to be the best-fitting models. The results also showed improvements over the widely used EGM2008 up to the spherical degree 270 for Turkey. The improvements of the GOCE models over the EGM2008 model are mostly seen in mountainous areas such as the Black sea, Aegean Sea, some parts of the Mediterranean, and South-eastern Anatolia regions with maximum improvements in the coastal areas of the Eastern Black Sea. The best-fitting GGMs to local gravity field identified with these measurements could be used for further geodetic and geophysical purposes in Turkey.

Interpretation of the lithospheric structure beneath the Indian Ocean from gravity gradient data

Global geoidal undulations are often used as the constraining parameter to model the mantle convection pattern, while gravity data are typically applied to interpret the lithospheric structure. In more recent studies, especially after launching the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite gravity-gradiometry mission, gravity gradient measurements have also been used in various geoscience applications. The main motivation of using gravity gradients is to provide a more conclusive information about a spatial localization of investigated phenomena. In geophysical studies, such implications are particularly related to a probably better detection of investigated lithospheric structures, such as active tectonic margins. In this study, we address this aspect by comparing interpretational characteristics from gravity and gravity gradient information. The Bouguer and mantle gravity gradients are used for this purpose to interpret the lithospheric structure beneath the Indian Ocean as well as the (adjacent) continental lithospheric structures (such as the East African Rift System). Our results confirm that gravity gradient more closely reproduces some tectonic and volcanic features, such as oceanic subductions, volcanic island arcs, and convergent continental tectonic margins. Similarly, mid-oceanic spreading ridges are localized slightly better in the gravity gradient map. Our findings also indicate that the interpretational quality cannot be improved by using directly observed gravity gradients. The reason is that these interpretations require applying gravimetric forward modelling techniques in order to enhance a particular lithospheric structure.

An adaptive topography correction method of gravity field and gradient measurements by polyhedral bodies

An adaptive topography correction method of gravity field and gradient measurements by polyhedral bodies

Proof-of-principle demonstration of vertical-gravity-gradient measurement using a single-proof-mass double-loop atom interferometer

We demonstrate a proof-of-principle of direct Earth gravity gradient measurement with an atom interferometer-based gravity gradiomter using a single proof mass of cold 87 rubidium atoms. The atomic gradiometer is implemented in the so-called double-loop configuration, hence providing a direct gravity gradient dependent phase shift insensitive do DC acceleration and constant rotation rate. The atom interferometer (AI) can be either operated as a gravimeter or a gradiomter by simply adding an extra Raman $\pi$-pulse. We demonstrate gravity gradient measurements first using a vibration isolation platform and second without seismic isolation using the correlation between the AI signal and the vibration signal measured by an auxilliary classical accelerometer. The simplicity of the experimental setup (a single atomic source and unique detection) and the immunity of the AI to rotation-induced contrast loss, make it a good candidate for onboard gravity gradient measurements.

A Folding Calculation Method Based on the Preconditioned Conjugate Gradient Inversion Algorithm of Gravity Gradient Tensor

To solve the non-uniqueness problem of gravity gradient inversion, we proposed a folding calculation method based on preconditioned conjugate gradient inversion. Compared with the original algorithm in which the entire study area is taken as the research subject and all grids are used simultaneously in the inversion, the proposed folding method divides the research area into several sub-areas. A prism unit from any of the four corner grids is selected for the first iteration, whose density anomaly result is taken as the initial density anomaly for the next iteration of the same sub-area. The folding in the left–right and up–down directions takes turns during the calculation until the inversion calculation has covered the entire research area. This folding algorithm demonstrates strong regularity. The inversion results of multiple synthetic models show that the folding calculation method performs multiple parameter corrections in the initial model. Meanwhile, on the basis that the relative fitting of standard errors of the observed values satisfies the convergence condition, the model errors are constrained, and thus, the model errors of the inversion results are consequently reduced. The 3-D density anomaly pattern over the Craton area in North China was obtained via a joint inversion of the four components ( $$\varvec{T}_{\text{xx}} ,$$ $$\varvec{T}_{\text{xz}} ,$$ $$\varvec{T}_{\text{yy}} ,$$ and $$\varvec{T}_{\text{zz}}$$ ) of the Gravity field and steady-state Ocean Circulation Explorer L2 gravity gradient after preprocessing. We compared the inversion results from the folding calculation method and the original method, and performed detailed analysis and discussion on the inversion results with existing geological and geophysical data. Our analysis shows that the improved calculation method is effectively applicable to the inversion of measured gravity gradient data, and the inversion results provide more detailed and reliable pattern information for the density anomaly.

A torsion balance device for measuring the gravity gradient

Based on the principle of torsion balance measuring gravity gradient, designed a torsion balance gravity gradiometer, consisting of a torsion balance system, an angle measurement system, an amplitude attenuation system, a turntable system, a vacuum container system. considering the stable time of torsion balance suspension system was too long, which had great impacted the efficiency of the gravity gradient measurement, designed an amplitude attenuation system in combination with PID control technology. Simulation results show that, the curvature and horizontal gravity gradient could be measured, the accuracy was as high as 0.5 E(1E = 1 × 10−9m/s2), and the limit efficiency of measuring a group of gravity gradients was better than an hour.

Understanding curvatures of the equipotential surface in gravity gradiometry

The concept of curvatures of equipotential surfaces is of theoretical and practical importance in gravity gradiometry because curvatures describe the shape of equipotential surfaces, which can yield information about the shape of the source. Although the fundamentals of curvatures are well-established, their connection to modern gravity gradiometry and the associated applications in exploration geophysics remain areas of active research. In particular, there is a misunderstanding in the calculation of the said curvatures directly from measured gravity gradient data that are now widely used in exploration geophysics. The error stems from the incorrect use of the formulas in a fixed user coordinate system that are only valid in a rotated coordinate system. We demonstrate that the gravity gradient tensor must be rotated to a local coordinate system whose vertical axis is aligned with the local anomalous gravity field direction so that the curvatures of the anomalous equipotential surface can be calculated correctly using these classic formulas. To facilitate practical application, we present theoretical and practical aspects related to coordinate systems and rotations of the gravity gradient tensor. We have also developed an approach for estimating local gravity for use in the curvature calculation by wavenumber-domain conversion from gradient tensors. The procedure may form a basis for developing new interpretation techniques in gravity gradient gradiometry based on curvatures.

The influence of installation angle of GGIs on full-tensor gravity gradient measurement

Gravity gradient plays an important role in many disciplines as a fundamental signal to reflect the information of the earth. Full-tensor gravity gradient measurement (FGGM) is an effective way to obtain the gravity gradient signal. In this paper, the installation mode of GGIs in FGGM is studied. It is expected that the accuracy of FGGM will be improved by optimizing the installation mode of GGIs. In addition, we analysed the relationship between GGIs’ installation angle and FGGM by establishing the measurement model of FGGM. Then the following conclusions was proved that there was no relationship between GGIs’ installation angle and the measurement result. This conclusion showed that there was no optimal angle for the GGIs’ installation in FGGM, and the installation angle only need to satisfy the relationship shown in the conclusion section of this paper. Finally, this conclusion was demonstrated by computer simulations.

Omission Error Analysis in Gravity Gradient Measurement

Gravity gradient plays an important role in many fields of science, and many methods are used to achieve the measurement of it. To improve measurement accuracy, various error analyses have been conducted in previous studies about positioning and orientation errors and system noise, among others. However, knowledge on the influence of omission errors from the theoretical models of gravity gradient measurement is limited. In this paper, we investigated omission errors in gravity gradient measurement, which was accomplished with the principle of differential acceleration. First, we determined the source of the omission errors to be the omission of high-order terms. Second, we calculated these terms on the basis of the Earth Gravitational Model 2008. Specifically, the expression of the partial derivative of the high order for the gravity potential in the spherical coordinates and the recursive equations for the high-order partial derivatives of the Legendre function were derived. Moreover, we transformed these high-order terms from the spherical coordinate system to the local north-oriented frame. The analysis led to three findings. First, a positive correlation was found between the omission errors and the distance between two measuring points. Second, the influences of the omission errors varied across different regions. Third, $\Gamma _{zz} $ was the least affected by the omission errors among the components $\Gamma _{xz} $ , $\Gamma _{yz} $ , and $\Gamma _{zz} $ . In conclusion, our study demonstrates that omission errors affect gravity gradient measurement.